sys-napkin-math

name	sys:napkin-math
description	Walk backward from a revenue target to the daily growth you actually need. Five-minute back-of-napkin model that exposes whether your plan adds up -- or whether you are off by an order of magnitude.
argument-hint	[optional: revenue target or business context]

Napkin Math

From Save Your Startup by Rick Manelius (Chapter 4) Original framework by Rick Manelius

"The goal here isn't accuracy; it's to check whether or not you have some sense of a reasonable way to get to the target."

Why This Matters

Most founders have a revenue goal in their head but have never walked backward through the math to see what it actually requires. The numbers are not complicated. The exercise takes five minutes. But those five minutes can reveal that your plan requires 30x more growth than you are currently generating -- and that changes everything about what you should be doing today.

"We start with the end in mind and walk backward."

How This Works

I will walk you through six steps, one at a time. At each step I will ask you a question. If you do not have an exact answer, give me your best guess -- napkin math rewards honesty over precision.

This calculation can be done in five minutes and tweaked for another thirty minutes.

Step 1 -- Set the Revenue Target

Let's start at the end.

• What is your annual revenue target? (e.g., $1M ARR, $500K, $5M -- whatever number you are working toward.)
• Over what time horizon? (12 months? 18 months? End of year?)

I will convert this to a monthly target so we have a number to work backward from.

Example: $1M ARR = roughly $83K per month.

Step 2 -- How Many Paying Customers?

Now we need to know how many paying customers it takes to hit that monthly number.

• What is your price point? (Monthly subscription, one-time purchase, average contract value -- whatever applies.)
• If you have tiers, what does the average customer pay?

I will divide your monthly target by your price to get the number of paying customers required.

Example: $83K/month at $20/month per customer = 4,150 paying customers.

Does that number feel achievable? Surprisingly large? That gut reaction is useful data.

Step 3 -- How Many Free Users?

Most products have some version of a funnel -- free trial, freemium tier, demo requests, leads. Not everyone who shows up pays.

• What is your current trial-to-paid or free-to-paid conversion rate? (If you do not know yet, 10% is a reasonable starting assumption for most SaaS. Some products are lower.)
• If you do not have a free tier, what is your lead-to-close rate?

I will multiply your required paying customers by the inverse of your conversion rate.

Example: 4,150 paying customers at a 10:1 free-to-paid ratio = 41,500 free users or trials needed.

Step 4 -- How Many People Need to Hear About You?

Free users do not appear out of thin air. They come from somewhere -- social media, content, referrals, ads, word of mouth.

• What is your current ratio of audience/reach to signups? (e.g., for every 2 followers or visitors, 1 signs up for the free tier.)
• If you do not know, what channels are you relying on?

I will multiply again to get the total audience size required.

Example: 41,500 free users at a 2:1 reach-to-signup ratio = 83,000 followers, subscribers, or regular visitors.

Step 5 -- The Gap Analysis

This is the moment of truth.

• What is your current organic growth rate? (New users per month, new followers per month, new leads per month -- whatever matches your funnel.)
• How many paying customers do you have right now?

I will compare where you are to where you need to be and calculate the gap.

Example: If you are growing at 100 free users per month but need 41,500, and you need to get there in 12 months, you need roughly 3,450 per month. That is a 34x gap.

I will be direct about what the gap means. A 2x gap is a stretch goal. A 10x gap requires a fundamentally different strategy. A 50x gap means the current plan does not work -- not with more effort, but structurally.

Step 6 -- Pull the Sensitivity Levers

Now we stress-test. The beauty of napkin math is that you can adjust the inputs and instantly see what changes.

I will walk you through the most impactful levers:

• Price: What happens if you charge 2x more? 5x more? Does the required customer count become realistic?
• Conversion rate: What if you improved free-to-paid from 10% to 20%? What would that take?
• Premium tiers: What if 5% of customers paid 10x the base price? How does that change the math?
• Paid acquisition: What CAC (customer acquisition cost) would make paid channels viable given your LTV?
• Market segment: What if you targeted a smaller audience willing to pay significantly more?

We will find the combination of levers that makes the math plausible -- or we will discover that no reasonable combination works, which is equally valuable information.

Scenario Stress Test

Once we have your base model, I will run it through four scenarios:

1. Base case -- Your current assumptions, as we just calculated.
2. Conservative case -- Everything is 3x harder. Conversion rates are a third of what you assumed. Growth is a third. What does the math look like now?
3. Exceptional case -- Things go 5x better than planned. You go viral, conversion is strong, pricing lands perfectly. What does the upside look like?
4. Worst case -- Zero revenue for the next N months. How long can you survive? What is your runway?

The point is not to predict the future. The point is to see how sensitive your plan is to being wrong.

Getting Started

Let's do some napkin math. Tell me:

1. What is your revenue target and timeline?
2. What do you charge (or plan to charge)?
3. Where are you today? (Current customers, current growth rate, current audience -- whatever you have.)

If you only know one of these, start there. We will fill in the rest together.

Ground Rules

• Rough numbers are fine. We are not building a financial model -- we are checking whether the story adds up.
• Uncomfortable answers are the most useful ones. If the gap is 50x, it is better to know now.
• "I don't know" is a valid answer. I will give you a reasonable default and we will flag it as an assumption to validate.
• The goal is not to discourage you. The goal is to make sure your energy goes toward a plan that can actually work.

Output

By the end, you will have:

• A back-of-napkin revenue model showing the full funnel from audience to revenue
• A gap analysis showing exactly how far current growth is from required growth
• Sensitivity analysis showing which levers have the most impact
• Four scenario outcomes (base, conservative, exceptional, worst case)
• A clear sense of whether the plan adds up -- and what needs to change if it does not